Study On The Static Topology Optimization Of Continuum Structure

With the developing of optimal algorithm and finite element method,scholars have already put forward various structural topology optimization method.Specifically,most of the space support structures are in the form of continuum,while the current topology optimization methods can realize the topology optimization process of continuum structure,but there is still room for improvement.For example,the gray-scale elements in the implicit description of Solid Isotropic Material with Penalization(SIMP)makes it impossible to obtain the 0-1 topology,and the initial component layout in the explicit description of Moving Morphable Components(MMC)method makes the optimization result fall into local solution,et al.So far,the thesis around the math model and simulation of continuum topology optimization algorithm.The typical algorithm and improve strategy are discussed.And it is applied to solve the static problem of continuum structure,realize engineering application to verify the engineering suitability of the proposed improved strategy.Among them,the specific research work is as follows:(1)Based on the review of the development of continuum structure static topology optimization,the implicit SIMP mathematical model based on OC(Optimality Criteria)algorithm and the explicit MMC mathematical model based on MMA(Moving Asymptotes Method)algorithm are derived in detail.And then the numerical instability phenomena of them are analyzed respectively.It is worth noting that the interpolation function characteristics of SIMP method makes it converge to the optimal topology quickly after several iterations.But this method has the “edge diffusion” phenomenon caused by gray-scale elements.And the optimization result of this method is affected by the accuracy of mesh generation,which will destroy the optimality of the structure when the serrated structure boundary is extracted and transformed into continuous smooth structure boundary.The MMC method,which takes the geometric structure boundary as the design variable,can directly realize the accurate identification of the geometric characteristics of the structure while obtaining the topological configuration.However,the number and layout of the initial components of this method determine which local optimal solution the final topological configuration will approach.For complex engineering structures,the initial components of MMC method are difficult to be perfectly arranged,which leads to the decrease of adaptability.(2)Aiming at the characteristics of these two methods,this paper develops an explicit and implicit hybrid structural topology optimization method.Otsu thresholding algorithm is introduced to maximize the topological configuration information under SIMP,so as to eliminate the influence of gray-scale elements.On this basis,morphological thought is used to construct a component,whose boundary is the inflection point of the skeleton,then the MMC method is used to complete the optimization work.By calculating the minimum compliance topology optimization problem of the 2D symmetrical short board and 3D cantilever beam numerical examples,and compared with the simple MMC method,the obtained topology boundary is smooth,complete and compliance value is smaller,which confirms the usefulness of this method.(3)The method is extended in engineering application.Specifically,the topology optimization of the main support frame in the Lidar ground test platform is carried out by adopting this method,and the results to contrast with those under ANSYS(Topology Optimization / Parameter Set module).The proposed method achieves the "win-win" results of structural weight(reduced by 2.64%)and the largest deformation(reduced by4.60%).Then a scale model(1:2)is established based on the static linear similarity theory,and a static loading test device is built.By loading step by step(5% increment of limit load 200N),the deformation of each structural member was recorded,and compared with the results of ANSYS(Static Structural module),the engineering reliability of the topology obtained by this method is proved.